Personal finance guides in plain words
- Guides
- 216
- Calculators
- 132
- Worked examples
- 1,307
- Comparisons
- 112
One concept per guide, answered in the first paragraph, with a working calculator on the same screen. No account needed for any of it.
Start here
- How FICA and take-home pay work$1,607
- How the leverage ratio works1.67 / 62.50% / 2.67
- The yield curve4.3992%
- How compound interest worksDoubles in 12 years
- How mortgages work$2,022.62 first payment
- Snowball against avalanche$296.37 saved
- How 401(k) matching works$2,400 a year
- Inflation and purchasing power$17,271.03 of today's goods
- Investment fees and drag22% below fee-free
- Time value of money$613.91 today
- How credit headroom works$5,600 of room
- Car finance and depreciation$30,392.28 owed
- How simple interest works$150
- How continuous compounding works8.3287%
- How the price to earnings ratio works20x
- How enterprise value works$130,000,000
- How return on equity works15%
- How mortgage affordability works$430,333.43
- How credit utilization works30%
- How the CAGR formula works10.29%
- How debt-to-income ratio works32%
- How APR and APY actually work5.116%
- How earnings yield works5%
- How NOPAT is calculated$75,000,000
- How EV/EBITDA works13x
- How PITI works$3,220.00
- How operating leverage worksDOL 3
- How DuPont analysis works15% ROE
- How debt-to-equity works1.67
- How market cap works$5,000,000,000
- How degree of financial leverage worksDFL 1.14
- How net profit margin works9%
- How the PEG ratio worksPEG 2
- How price to book works2.50x
- How total return works8%
- How tax brackets work$8,160
- How required minimum distributions work$20,000
- How Social Security benefits work$2,345.80
- How cash-on-cash return works2.45%
- How a HELOC works$333.33 a month
- How ETFs work$38,696.84
- How a mortgage escrow works$650 a month
- How Series I bonds work4.218%
Class and household
How simple interest works
Simple interest is principal times rate times years. On \$1,000 at 5 percent for 3 years that is \$150, because the rate never sees interest already earned.
How hourly pay becomes a salary
Annual pay is hourly wage times hours a week times weeks a year. At \$15 an hour for 40 hours across 52 weeks that is \$31,200 a year, or \$600 a week, before tax.
How the 50/30/20 budget split works
The 50/30/20 rule sends half of take-home pay to needs, 30 percent to wants, and 20 percent to saving. On \$4,500 take-home that is \$2,250, \$1,350 and \$900.
How budgeting works: plan, split, saving rate
What a budget is for, fixed against variable costs, where the 50/30/20 rule breaks down, zero-based budgeting, and what a saving rate does and does not predict.
Emergency funds: how to size and build one
What an emergency fund covers, how to size it from your own essential monthly costs rather than a generic month count, and why it stays liquid even at a lower rate.
How credit scores work and what moves them
What a credit score measures, which factors carry the most weight, why utilisation is the fastest lever a borrower has, and how a score differs from debt-to-income.
How credit cards charge interest
How a card turns an APR into a daily rate, why paying the statement balance in full usually costs nothing, what a partial payment does, and why cash advances start charging at once.
How student loans work in the United States
How interest accrues before repayment starts, what capitalisation adds to the balance, why a standard and an income-driven plan produce different totals, and what refinancing gives up.
What net worth means and how to track it
Net worth is what you own minus what you owe. Which assets to count and at what value, whether a home and a car belong on the list, and why the trend beats one reading.
How FICA and take-home pay work
FICA is 6.2 percent Social Security plus 1.45 percent Medicare. On a \$2,000 weekly check with 12 percent federal withholding, take-home is \$1,607.
How credit utilization works
Credit utilization is the reported revolving balance divided by the revolving limit. \$2,400 on an \$8,000 limit is 30 percent, and paying in full may still show a balance.
How credit headroom works
Credit headroom is the revolving limit minus the reported balance. \$2,400 on an \$8,000 limit leaves \$5,600 of room. Utilisation is 30 percent. This page owns the \$5,600.
Credit reports and how to fix errors
What a United States credit report contains, who supplies the data, why errors are common, and how a dispute works with both the agency and the company that reported it.
Types of savings account, compared
Checking, savings, high-yield savings, money market accounts and certificates of deposit: what each one trades away for a higher rate, and why the yield beats the rate.
How compound interest works
Interest that earns interest, explained with worked numbers: the formula, what an early start is really worth, the rule of 72, and what compounding frequency changes.
How the CAGR formula works
CAGR is the one steady yearly rate that turns a start value into an end value. \$10,000 to \$18,000 over 6 years is 10.29 percent a year, not the average of the yearly returns.
How APR and APY actually work
APR is the yearly rate before compounding. APY is the same rate after it. A 5 percent APR compounded monthly is a 5.116 percent APY, so \$10,000 earns \$511.62 rather than \$500.
How continuous compounding works
Continuous compounding is the ceiling a quoted rate approaches. An 8 percent rate yields 8.3287 percent, so \$25,000 earns \$2,082.18 rather than \$2,000.
How time-weighted return works
Time-weighted return is the compound growth of one unit of money, with cash flows stripped out. On a stretch with no deposits it is the CAGR: \$10,000 to \$18,000 over 6 years is 10.29 percent.
How price return works
Price return is the finish minus the start, over the start. A \$100 holding that ends at \$105 returns 5 percent from price. The \$3 of income is a separate slice.
Time value of money: present and future value
Why a dollar today is worth more than a dollar later, and by how much. Present value, future value, discount factors and how to pick the rate that prices the wait.
Opportunity cost of money: what you give up
Every dollar has a next best use. How to price what a purchase, a cash pile or an unpaid debt gives up, how to pick the rate you compare against, and when to bother.
Dollar cost averaging, explained
Buying a fixed amount on a schedule: why the cost per unit lands at or below the average price, why investing a lump sum at once usually finishes ahead, and what spreading buys.
Behavioural biases in money decisions
Loss aversion, mental accounting, anchoring, recency, confirmation and sunk cost, each with a money example, and why rules set in advance beat willpower.
Borrowing and credit
How a mortgage works, from lien to payment
What the lender's lien actually secures, how loan to value and escrow work, what discount points buy, and why the first years of a mortgage are almost all interest.
How amortisation works, payment by payment
Why a level loan payment is nearly all interest at the start, how the split shifts every month, what an extra payment removes, and what a shorter term does.
How extra mortgage payments work
What an extra amount paid against principal does to a mortgage: months taken off the term, interest not paid, and why the first extra dollars buy more time than the later ones.
How private mortgage insurance works
PMI is a lender-required premium when the down payment is under 20 percent. What it is charged on, when it cancels at 80 percent of original price, and why it is not a higher mortgage rate.
How mortgage points work
Discount points are prepaid interest paid at closing to cut the contract rate. How the cash-flow break-even is counted in months, and why refinancing resets that clock.
Payday loans and high cost credit
Why a fee that looks small over two weeks annualises into a triple digit APR, how the rollover cycle repeats it, and what the alternatives actually cost.
How refinancing break-even works
Refinance break-even is closing costs over the monthly saving. Moving \$300,000 from 7.25 percent with 25 years left to 6.25 percent over 30 years saves \$321.27 a month.
How mortgage affordability works
Lenders cap total monthly debt at a share of gross pay. On \$9,000 a month with \$650 of other debts, a 43 percent rule leaves \$2,720.00 for principal and interest.
How credit card payoff works
Pay a flat \$125 a month on a \$6,000 card at 22.9 percent and it takes 132 months, costing \$10,378.84 in interest. Month one charges \$114.50 of that \$125.
How car loan payments work
A car loan uses the level-payment formula. Finance \$32,000 at 8.5 percent over 5 years and the payment is \$656.53 a month, with \$7,391.74 of interest.
How student loan payoff works
Owe \$35,000 at 5.5 percent over 10 years and the scheduled payment is \$379.84. Pay \$500 a month instead and the loan clears in 85 payments, not 120.
How debt-to-income ratio works
DTI is monthly debt payments over gross monthly income. Debts of \$2,400.17 against pay of \$7,500 are 32.00 percent, with \$824.83 of room under a 43 percent ceiling.
How loan-to-value ratio works
Loan-to-value is the loan divided by the property value. On a \$400,000 home with \$20,000 down the loan is \$380,000 and LTV is 95 percent. At 80 percent, conventional PMI drops out.
How PITI works on a mortgage
PITI is the housing payment: principal, interest, tax and insurance. On \$9,000 a month at a 43 percent back-end cap, PITI is \$3,220.00 and principal and interest are \$2,720.00.
How home equity works
Home equity at purchase is the down payment: price minus the loan. On a \$400,000 home with \$20,000 down, the loan is \$380,000, LTV is 95 percent, and starting equity is 5 percent.
How a HELOC actually works
A HELOC is a revolving loan secured by home equity. See how an interest only draw payment is calculated, why its rate can move, and what changes in repayment.
How ARM mortgages work
An adjustable rate mortgage starts with a fixed rate, then resets from an index and margin. Learn how reset dates, payment changes and rate caps fit together.
How a mortgage escrow works
A mortgage escrow collects one twelfth of projected property tax and insurance each month. Learn how the impound account, annual analysis and shortages work.
Debt snowball vs avalanche: the numbers
The avalanche pays the highest rate first and the snowball the smallest balance first. Two cards, one budget, both orders run in full, and what sets the size of the gap.
Car finance, depreciation, negative equity
Why a loan against a car that is losing value turns into negative equity, how depreciation front-loads, what a longer term really costs, and what the payment hides.
Renting against buying a home
What each side costs and never returns, why the mortgage payment is the wrong number to compare, how the break-even horizon works, and what borrowing does to the risk.
How car leases work
A lease pays for depreciation plus a finance charge. On a \$30,000 car with an \$18,000 residual over 36 months that is \$333.33 plus \$60.
How biweekly mortgages work
Half a payment every fortnight makes 26 half payments a year. On \$250,000 at 6.5 percent that clears the loan in 628 periods and saves \$73,434.82.
How interest-only mortgages work
An interest-only payment covers the charge and nothing else. \$400,000 at 6.5 percent costs \$2,166.67 a month and the balance never moves.
How a remaining loan balance works
After 60 payments of \$1,580.17 on a \$250,000 loan at 6.5 percent, \$234,027.44 is still owed. Early payments are mostly interest.
How money factor works
A money factor is a lease rate in disguise. Multiply it by 2400 to read it as an APR: 0.00125 is 3 percent, and 0.002 is 4.8 percent.
How years to payoff works
Payoff time depends on how much of the payment survives the interest. \$12,000 at 21.99 percent with \$400 a month takes 44 months.
How down payments work
A down payment sets the loan, not just the cash. 20 percent of \$400,000 is \$80,000 down and a \$320,000 loan; 5 percent leaves \$380,000 to borrow.
Saving and planning
How present value works
Present value is what a future cash flow is worth today at a stated rate. How discounting undoes growth, how a payment stream is a stack of lumps, and why the rate and the period have to match.
How a savings goal payment is set
A savings-goal deposit is what the target still needs, divided by the annuity factor. Reaching \$30,000 in 5 years at 4 percent monthly takes \$452.50 a month.
How the rule of 72 works
The rule of 72 estimates doubling time: 72 divided by the annual rate in percentage points. At 7 percent it gives 10.2857 years against an exact 10.2448.
How expense ratios drag returns
A fund fee comes off the rate your money compounds at. Start with \$10,000, add \$300 a month for 30 years at 7 percent: a 0.65 percent fee leaves \$389,198.79.
How FIRE numbers work
A FIRE number is annual spending divided by a withdrawal rate. Why 4 percent is 25 times spending, how years to the pile are counted at one constant return, and what the identity is silent on.
How real returns work
A real return is what a return buys after inflation. Divide, do not subtract. At 7 percent with 3.2 percent inflation the real return is 3.68 percent a year, not the 3.80 percent subtraction gives.
How inflation factors work
Inflation runs two ways on one sum. At 3 percent, what costs \$50,000 today costs \$67,195.82 in 10 years, and \$50,000 of cash buys what \$37,204.70 buys now, 25.59 percent less.
How annuity future value works
The future value of an annuity is what a run of level payments grows to. \$500 a month for 20 years at 6 percent compounded monthly reaches \$231,020.45 if paid at the end of each month.
How FDIC insurance works
FDIC insurance covers eligible deposits per depositor, per insured bank, per ownership category. Learn how accounts combine, what products qualify and how to calculate covered and uninsured balances.
How money market funds work
Money market funds pool short-term debt, pass income to shareholders and often aim for a stable 1.00 NAV. Learn what drives yield, liquidity and risk, and why a fund is not a bank deposit.
How Series I bonds work
Series I savings bonds combine a fixed rate with a twice-yearly inflation rate. Learn the composite-rate formula, reset schedule, compounding, redemption rules and tax treatment.
How a CD ladder works
A CD ladder splits cash across certificates that mature on a stagger. Each rung compounds at its own rate and term. This sheet prices two rungs so the identity is visible.
How a 529 education plan works
A 529 plan is a wrapper for education saving. This sheet compounds an illustrative contribution so the growth identity is visible, not as a statutory cap or a school bill.
How a health savings account works
An HSA can deduct eligible contributions, shelter investment growth, and exempt qualified medical withdrawals. See the three tax steps.
Inflation and purchasing power explained
What inflation does to money over time, why a real return divides rather than subtracts, and how an account paying under inflation loses ground while the balance rises.
How annuities work
An annuity swaps a sum of money for an income. How the pool pays, why a payout rate is not a return, and what fixed, variable and deferred contracts each change.
How coast FIRE works
Coast FIRE is the point where growth alone reaches your target. \$200,000 at 7 percent for 20 years becomes \$773,936.89 without another contribution.
How a perpetuity is priced
A payment that never ends has a finite value. \$1,000 a year discounted at 5 percent is worth \$20,000, because later payments discount to almost nothing.
Annuity present value explained
Ten payments of \$1,000 discounted at 6 percent are worth \$7,360.09 today. Each payment is divided by growth for every year you wait for it.
How sinking fund deposits work
A sinking fund solves for the deposit that reaches a target. \$10,000 in five years at 6 percent needs \$1,773.96 a year, because the early deposits earn.
How a savings rate is measured
A savings rate is money saved over income. \$15,000 on \$75,000 is 20 percent, and the definitions you pick change the answer more than the habits do.
Investing
Risk and return: the trade-off explained
Why higher expected return demands more risk, what risk means as a spread of outcomes, how the risk premium sits above the risk-free rate, and what volatility costs.
How diversification lowers risk
Why holding assets that do not move together lowers risk without lowering expected return, what correlation means in plain words, and what diversification cannot protect you from.
Asset allocation: how the mix drives risk
How a portfolio splits across stocks, bonds and cash, why the mix explains most of the variation in returns over time, and how horizon and risk capacity set it.
The yield curve: shape, slope and inversion
What the yield curve plots, why it normally slopes up, what an inverted curve says about future interest rates, and how much weight its recession record deserves.
How portfolio rebalancing works
Rebalancing sells what has grown and buys what has not, to restore a target mix. Why drift raises risk silently, calendar against threshold rules, tax friction, and what it really pays.
Index funds vs active management
Why the average actively managed dollar trails the market by its costs, what an index fund actually holds, and what one point of yearly fee does over 30 years.
How stocks work: shares, profit and price
What a share of stock actually is: a claim on the profit left after everyone else is paid, why dividends and retained earnings are the same dollar, and what a price represents.
How bonds work: coupon, price and yield
What a bond is, how face value, coupon and maturity fit together, why prices fall when interest rates rise, what duration measures, and where bondholders rank if a borrower fails.
How bond pricing works
A bond is the present value of its coupons plus face, discounted at the market rate. A \$1,000.00 bond with a 5 percent coupon twice a year for 10 years is worth \$1,000.00 at a 5 percent market rate.
How bond duration works
Macaulay duration is the present-value-weighted wait for a bond's cash flows. A 5-year 5 percent par bond of \$1,000 has a Macaulay duration of 4.55 years and a DV01 of \$0.43.
How bond premium and discount work
A bond prices at a discount when the market rate sits above the coupon, and at a premium when it sits below. The same 5 percent 10-year bond is \$857.88 at 7 percent and \$1,171.69 at 3 percent.
How market capitalisation works
Market cap is share price times shares outstanding. A \$50 share on 100,000,000 shares is \$5,000,000,000. P/E is that pile over total earnings, the same 20 as price over EPS.
How the Gordon growth model works
Gordon growth prices a stock as next year's dividend over required return minus growth. A \$2.00 dividend just paid, growing at 4 percent, with a 9 percent required return, is worth \$41.60.
How two-stage DCF works
Two-stage DCF values a firm as an explicit free-cash-flow forecast plus a Gordon-growth terminal value. Why most enterprise value sits after the forecast, and why growth must stay below WACC.
How the price to earnings ratio works
P/E is share price divided by earnings per share. A \$50 share on \$2.50 of earnings is 20 times, and a lower P/E is not always a cheaper share.
How earnings per share works
Earnings per share is total earnings divided by shares outstanding. \$250,000,000 of earnings on 100,000,000 shares is \$2.50 a share. Price over that \$2.50 is a P/E of 20.
How earnings yield works
Earnings yield is EPS over price, which is 1 over the P/E multiple. A \$50 share on \$2.50 of earnings is 20 times and a 5 percent yield. Same sheet as the P/E calculator, flipped.
How yield to maturity works
Yield to maturity is the discount rate that prices every remaining coupon plus face. A 5 percent coupon bond at \$857.88 has a 7 percent YTM and a 5.83 percent current yield.
How current yield works
Current yield is the annual coupon divided by the price you pay. A 5 percent coupon bond yields 5.00 percent at par, 5.83 percent at \$857.88, and 4.27 percent at a premium.
How dividend yield works
Dividend yield is cash paid over price. Trailing yield uses the dividend just paid. Implied yield uses next year, and on Gordon growth it equals required return minus growth.
How the PEG ratio works
PEG is P/E divided by expected EPS growth in percent. A \$50 share on \$2.50 of earnings growing at 10 percent is a P/E of 20 and a PEG of 2.
How price to book works
P/B is price over book value per share, which is market cap over book equity. A \$50 share on \$20 of book is 2.50 times on \$5,000,000,000 of market cap.
How book value per share works
BVPS is book equity divided by shares. \$2,000,000,000 of book on 100,000,000 shares is \$20 a share. A \$50 price on that book is a P/B of 2.50.
How price to sales works
P/S is price over sales per share, which is market cap over sales. A \$50 share on \$25 of sales is 2 times on \$5,000,000,000 of market cap.
How total return works
Total return is price change plus income, over the start. A \$100 holding that ends at \$105 and pays \$3 returns 8 percent: 5 percent from price and 3 percent from income.
How sales per share works
Sales per share is sales divided by shares. \$2,500,000,000 of sales on 100,000,000 shares is \$25 a share. A \$50 price on that \$25 is a P/S of 2.
How income yield works
Income yield is cash received over the start of the window. On a \$100 holding that pays \$3, that slice is 3 percent. Income is added once, not reinvested.
How free cash flow yield works
FCF yield is unlevered free cash flow over market cap. On \$55,000,000 of FCF and \$1,100,000,000 of market cap it is 5 percent. It is a cash yield, not an earnings yield.
How money-weighted return works
Money-weighted return is the IRR of dated cash flows. Spend \$10,000, collect \$3,000 a year for five years, and the money-weighted return is 15.24 percent.
How an offer premium is measured
Offer premium is the offer price minus the unaffected price, over the unaffected price. A \$52 bid on a \$40 close is a 30 percent premium, or \$12 a share.
How tax-equivalent yield works
Tax-equivalent yield is the taxable yield that matches a tax-exempt yield after tax. A 3.50 percent municipal at a 32 percent federal rate equals a 5.15 percent taxable yield.
Volatility drag: why averages overstate growth
Why a run of returns that varied compounds to less than its arithmetic average, why the gap grows with the square of the spread, and why a fund tracking twice an index daily misses over a year.
How ETFs actually work
An ETF is a basket that trades like a share. See how creation and redemption keep its price near NAV, and how its annual fee compounds against returns.
How fund NAV works
Net asset value turns a fund's assets and liabilities into a per-share value. Learn the formula, the daily calculation, and why an ETF can trade above or below it.
How TIPS actually work
TIPS adjust principal with consumer prices and apply a fixed coupon rate to that changing balance. See how inflation changes principal, interest, market price, maturity value and taxable income.
How Treasury bills are priced
A T-bill is a short-term Treasury sold at a discount to face. Price is face minus the discount-rate times face times days over 360. The holder then receives face at maturity.
How the Sharpe ratio works
The Sharpe ratio divides return above a risk-free rate by return volatility. Learn the formula, compare two portfolios, and read what the result does and does not measure.
How the CAPM formula works
CAPM combines a risk-free rate, market risk premium and beta to estimate a required return. See the formula, two calculations, and what beta contributes.
How a call option works
A long call gives its buyer the right to buy an asset at a strike price. Learn intrinsic value, expiry profit, the premium, break-even and the buyer's risk.
How a put option works
A long put is the right to sell at a strike. Intrinsic value at expiry is the amount strike exceeds spot, or zero. Profit subtracts the premium paid.
How a stock split works
A stock split multiplies shares and divides the price per share without changing market value. See the arithmetic, chart adjustments, EPS effects and reverse splits.
How margin trading works
Margin trading combines investor cash with a broker loan. Learn how initial margin sets buying power, how account equity moves and why maintenance calls can force action.
What investment fees really cost
Percentage fees are charged on your balance, not your gain, so they are paid in losing years too. What expense ratios, platform fees, spreads and advice fees really cost over time.
What a stock index is, and how it is weighted
A stock index is a rule for choosing companies and weighting them. How market value, price and equal weighting differ, what reconstitution changes, and why an index is not the economy.
How DV01 works
DV01 is modified duration times price over 10,000. A 5-year par bond of \$1,000 has a DV01 of \$0.43. Macaulay is a wait. DV01 is money.
How the Graham number works
The Graham number caps price at the square root of 22.5 times EPS times book value. With \$2 and \$20 that ceiling is \$30 a share.
How the Sortino ratio works
Sortino divides excess return by downside deviation, so only losses count as risk. A 10 percent return over a 3 percent target with 8 points of downside is 0.875.
How modified duration works
Modified duration turns a weighted wait into a price sensitivity. A Macaulay duration of 7.5 years at a 6 percent semiannual yield is 7.2816.
Corporate finance
How WACC is calculated
The weighted average cost of capital blends equity and after-tax debt by market value. The WACC formula, the tax term on debt, and why cheaper debt does not stay cheaper as the mix shifts.
How NPV and IRR work
NPV and IRR are one equation asked two ways: a value at a rate you choose, or the rate that drives that value to zero. They agree on accept or reject. Ranking is a different question, and NPV decides.
How the leverage ratio works
The three leverage ratio formulas from one balance sheet: debt-to-equity, debt-to-assets and the equity multiplier, plus what a fall in asset values does to equity.
How return on equity (ROE) works
ROE is net income over book equity. On \$15,000,000 of profit and \$100,000,000 of equity it is 15 percent, and financial leverage sits inside that rate.
How the cash conversion cycle works
CCC is days sales plus days inventory, minus days payable. 45 plus 60 minus 30 is 75 days, and a negative cycle means suppliers are funding the firm.
How interest coverage works
Interest coverage is EBIT divided by interest expense. On \$80,000,000 of EBIT and \$10,000,000 of interest it is 8 times, and a zero interest line is not infinity.
Cost of capital: the rate a project clears
The cost of capital is the return an investment must beat, not a bill a company pays. Why equity costs more than debt, what the interest deduction is worth, and where one firm-wide rate misleads.
How to read financial statements
The three statements and what each answers: the balance sheet at one date, the income statement over a period, and the cash flow statement that shows why profit is not cash.
How break-even analysis works
Break-even units are fixed costs divided by contribution margin. With \$24,000 of fixed costs, a \$35 price and \$20 of variable cost, you break even at 1,600 units.
How the payback period works
Payback is how long a project takes to hand back the cash it cost. A \$60,000 machine returning \$18,000 a year pays for itself in 3.33 years. Later cash is ignored.
How the current ratio works
The current ratio is current assets over current liabilities. With \$600,000 of current assets and \$400,000 of liabilities it is 1.50. Take out \$160,000 of inventory and the quick ratio is 1.10.
How enterprise value works
Enterprise value is equity plus interest-bearing debt minus surplus cash. On \$100,000,000 of equity, \$40,000,000 of debt and \$10,000,000 of cash, EV is \$130,000,000.
How free cash flow is built
Unlevered free cash flow is NOPAT plus D&A, minus capex, minus the increase in working capital. On \$100,000,000 of EBIT at 25 percent tax, FCF is \$55,000,000.
How equity value from EV works
Equity is enterprise value minus net debt. On \$130,000,000 of EV, \$40,000,000 of debt and \$10,000,000 of cash, equity is \$100,000,000. That EV is 13 times \$10,000,000 of EBITDA.
How return on invested capital works
ROIC is NOPAT over invested capital. On \$100,000,000 of EBIT at 25 percent tax and \$500,000,000 of capital, NOPAT is \$75,000,000 and ROIC is 15 percent.
How NOPAT is calculated
NOPAT is EBIT after tax, before interest. On \$100,000,000 of EBIT at 25 percent tax it is \$75,000,000. That is the numerator of ROIC, not net income and not free cash flow.
How unlevered beta works
Unlevered beta is equity beta divided by one plus after-tax D/E. An equity beta of 1.2, a 25 percent tax rate, and D/E of 0.5 produce an asset beta of 0.8727.
How after-tax cost of debt works
After-tax cost of debt is the interest rate times one minus the tax rate. At 5 percent and 25 percent tax that is 3.75 percent, the debt term inside WACC.
How the equity multiplier works
The equity multiplier is assets over equity. On \$800,000 of assets and \$500,000 of debt it is 2.67, so a 10 percent fall in assets is a 26.67 percent fall in equity.
How net debt is calculated
Net debt is interest-bearing debt minus surplus cash. On \$40,000,000 of debt and \$10,000,000 of cash it is \$30,000,000, the bridge from equity value to enterprise value.
How working capital works
Working capital is current assets minus current liabilities. With \$600,000 of current assets and \$400,000 of bills it is \$200,000, the dollar gap behind a 1.50 current ratio.
How gross margin works
Gross margin is gross profit over revenue. \$2,000,000 of sales minus \$1,300,000 of cost of goods leaves \$700,000, a 35 percent margin. It is not earnings and it is not a liquidity ratio.
How the quick ratio works
The quick ratio is current assets minus inventory, over current liabilities. On \$600,000 of current assets, \$160,000 of stock and \$400,000 of bills it is 1.10.
How contribution margin works
Contribution margin is price minus variable cost per unit. At a \$35 price and \$20 of variable cost the margin is \$15, so \$24,000 of fixed costs break even at 1,600 units.
How operating leverage works
Degree of operating leverage is contribution over EBIT. On the break-even teaching sheet, 2,400 units print a DOL of 3 and 3,200 units print 2, because EBIT has thickened.
How margin of safety works
Margin of safety is how far sales sit above break-even. At 2,400 units against a 1,600-unit crossing, the unit margin of safety is 33.33 percent. At 3,200 units it is 50 percent.
How EV/EBITDA works
EV/EBITDA is enterprise value over EBITDA. On \$130,000,000 of EV and \$10,000,000 of EBITDA the multiple is 13 times. Raise EBITDA to \$13,000,000 and the same EV is 10 times.
How the debt-to-equity ratio works
Debt-to-equity is debt divided by equity. On \$800,000 of assets and \$500,000 of debt, equity is \$300,000 and the ratio is 1.67. Plus one, that is the 2.67 equity multiplier.
How the debt-to-assets ratio works
Debt-to-assets is debt divided by total assets. On \$800,000 of assets and \$500,000 of debt it is 62.50 percent. The rest, 37.5 percent, is equity's share, and the fall that wipes equity out.
How DuPont analysis works
DuPont splits ROE into net margin, asset turnover and the equity multiplier. On \$45,000 of profit, \$500,000 of sales and \$800,000 of assets against \$300,000 of equity, the product is 15 percent.
How return on assets works
ROA is net income over total assets. On \$45,000 of profit and \$800,000 of assets it is 5.625 percent. Times the 2.67 equity multiplier, that is the 15 percent ROE on the same sheet.
How asset turnover works
Asset turnover is sales divided by assets. On \$500,000 of sales and \$800,000 of assets it is 0.625. Times a 9 percent net margin, that is the 5.625 percent ROA on the same DuPont sheet.
How net profit margin works
Net profit margin is net income over sales. On \$45,000 of profit and \$500,000 of sales it is 9 percent. Times 0.625 asset turnover, that is the 5.625 percent ROA on the same DuPont sheet.
How EBITDA is calculated
EBITDA is EBIT plus depreciation and amortisation. On \$100,000,000 of EBIT and \$20,000,000 of D&A, EBITDA is \$120,000,000. Free cash flow on that sheet is \$55,000,000. EBITDA is not cash.
How the profitability index works
The profitability index is present value of inflows over the outlay. Five receipts of \$3,000 against a \$10,000 cost are worth \$11,978.13 at 8 percent, so the index is 1.20 and NPV is \$1,978.13.
How the operating cycle works
The operating cycle is days sales plus days inventory, before payables. 45 plus 60 is 105 days. CCC then subtracts DPO: 105 minus 30 is 75 days.
How inventory turnover works
Inventory turnover is 365 divided by days inventory outstanding. A DIO of 60 is 6.08 turns a year. The same DIO sits inside a 105 day operating cycle when DSO is 45.
How days sales outstanding works
DSO is how long customers take to pay. On the cash cycle sheet it is 45 days. Plus 60 days of inventory that is a 105 day operating cycle, and minus 30 of payables a 75 day CCC.
How days payable outstanding works
DPO is how long the firm takes to pay suppliers. On the cash cycle sheet it is 30 days. A 105 day operating cycle minus that 30 is a 75 day CCC. Stretch it to 100 and CCC turns negative.
How receivables turnover works
Receivables turnover is 365 divided by days sales outstanding. A DSO of 45 is 8.11 turns a year. The same 45 sits inside a 105 day operating cycle when DIO is 60.
How payables turnover works
Payables turnover is 365 divided by days payable outstanding. A DPO of 30 is 12.17 turns a year. The same 30 is the gap between a 105 day operating cycle and a 75 day CCC.
How degree of financial leverage works
Degree of financial leverage is EBIT over EBIT minus interest. On \$80,000,000 of EBIT and \$10,000,000 of interest, coverage is 8 times and DFL is 1.14, which is 8 over 7.
How EV/sales works
EV/sales is enterprise value over sales. On \$130,000,000 of EV and \$65,000,000 of sales the multiple is 2 times. Raise sales to \$130,000,000 and the same EV is 1 times.
How operating margin works
Operating margin is EBIT over sales. On \$100,000,000 of EBIT and \$500,000,000 of sales it is 20 percent. Add \$20,000,000 of D&A and EBITDA is \$120,000,000.
How EBITDA margin works
EBITDA margin is EBITDA over sales. On \$120,000,000 of EBITDA and \$500,000,000 of sales it is 24 percent. Operating margin on that sheet is 20 percent.
How the payout ratio works
Payout is dividends over net income. On \$18,000 of dividends and \$45,000 of profit it is 40 percent. Retention is 60 percent on \$300,000 of equity.
How the retention ratio works
Retention is 1 minus payout. On \$45,000 of profit and \$18,000 of dividends, b is 60 percent. g is ROE times b if payout, margin and the equity multiplier stay put.
How sustainable growth works
Sustainable growth is ROE times the retention ratio. On 15 percent ROE and 60 percent retained, g is 9 percent. That holds if payout, margin and the equity multiplier stay put.
How the cash ratio works
The cash ratio is cash over current liabilities. On \$200,000 of cash and \$400,000 of bills it is 0.50. The current ratio on that denominator keeps receivables and inventory in.
How the Hamada factor works
The Hamada factor is 1 plus after-tax D/E. Equity beta 1.2, tax 25 percent, D/E 0.5: the factor is 1.375. Asset beta is equity beta over that 1.375.
How implied cap value works
Implied value is NOI divided by a comparison cap. \$36,000 of income at 6 percent is worth \$600,000. Offered at \$480,000, the gap is \$120,000 below that value.
How the interest residual works
The interest residual is EBIT minus interest. On \$80,000,000 of EBIT and \$10,000,000 of interest it is \$70,000,000. Coverage is 8 times. DFL is 8 over 7.
Financial ratios, and what they miss
The four families of financial ratio, what each one answers, and why nearly every ratio needs a comparable before it means anything: the same company last year, or a rival.
Taxes and retirement
Tax-advantaged accounts: how they work
How tax deferred and tax exempt accounts differ, why sheltering the growth does most of the work, and how to weigh paying tax now against paying it later.
How 401(k) matching works
A 401(k) match is a stated rate on a stated slice of pay. How the cap works, what is left unclaimed if you defer less, and what that leftover stream grows to if it is invested.
Safe withdrawal rates and what they assume
What a safe withdrawal rate is, the historical backtests it comes from, and the assumptions that move it: horizon, allocation, fees, taxes and whether spending flexes.
How sequence of returns risk works
The order returns arrive in changes nothing while a portfolio sits still, and a great deal once you withdraw from it. Worked numbers, and why the years around retirement matter most.
How investments are taxed
Income against capital gains, realised against unrealised, why a holding period can change the rate, why funds distribute gains you did not choose, and what a wrapper changes.
How tax brackets actually work
Tax brackets stack slices of income at rising rates. See why a 22 percent marginal rate does not apply to the whole income.
How effective tax rate works
Effective tax rate is total tax divided by the income base you name. It is an average, not the statutory rate on the last dollar of a stacked schedule.
How tax-loss harvesting works
Tax-loss harvesting realises a loss in a taxable account so it can offset gains or a limited amount of ordinary income. The tax saved is the loss times the rate that would have applied.
How a Roth conversion works
A Roth conversion moves pre-tax retirement money into a Roth account and treats the converted amount as taxable income this year. The tax is the converted dollars times the rate on those dollars.
How self-employment tax works
Self-employment tax is Social Security and Medicare on net earnings from self-employment. The base is 92.35 percent of net, and the combined rate on that base is 15.3 percent.
How required minimum distributions work
A required minimum distribution is the prior year-end retirement balance divided by an IRS life-expectancy factor. See the formula, timing, tax treatment and two worked examples.
How Social Security benefits work
Social Security converts indexed career earnings into a progressive monthly insurance benefit. Follow AIME through the bend-point formula, then see how claiming age changes the payment.
How claiming age changes Social Security
Claiming before full retirement age cuts PIA by a factor. Claiming later raises it, up to a delayed-retirement cap. This sheet multiplies a teaching PIA by 0.70 and by 1.24.
How the QBI deduction works
The qualified business income deduction is a percent of QBI in the simple case. Wage, property, and taxable-income caps can cut it. This sheet is the uncapped percent.
How net investment income tax works
The net investment income tax is 3.8 percent of the lesser of net investment income and the excess of MAGI over a threshold. This sheet is 3.8 percent of a teaching NII amount.
How the gift tax annual exclusion works
The annual gift-tax exclusion is a teaching cap on this sheet. Gifts at or under the cap use none of a lifetime exemption. Gifts above it create an excess that must be accounted for.
How taxable Social Security works
Provisional income decides how much of a benefit is taxed. With \$20,000 of AGI and \$18,000 of benefits, \$2,000 becomes taxable.
How the home sale exclusion works
The exclusion removes gain, not proceeds. A \$320,000 gain with a \$250,000 cap leaves \$70,000 taxable, whatever the house sold for.
How after-tax returns work
Tax takes a share of the return, not of the balance. An 8 percent return at a 22 percent rate leaves 6.24 percent, a drag of 1.76 points.
How additional Medicare tax works
The 0.9 percent surcharge applies only above a threshold. On \$250,000 of wages against a \$200,000 threshold, the tax is \$450.
How capital gains tax is computed
Tax applies to the gain, not the proceeds. Selling for \$40,000 what cost \$25,000 is a \$15,000 gain, and 15 percent of that is \$2,250.
Rental property
How cap rates work
Cap rate is net operating income over price. The same income at a comparison cap is a value, which is how two properties are compared without mixing in a mortgage or a tax bracket.
How rental cash flow is calculated
Rental cash flow is rent after vacancy, operating costs, and debt service. It can be positive or negative. Net operating income is the line before the loan payment.
How cash-on-cash return works
Cash-on-cash return is annual cash flow divided by cash invested. It is a cash yield on the equity cheque, not a cap rate and not an IRR.
How gross rent multiplier works
Gross rent multiplier is purchase price divided by annual scheduled rent. It ignores vacancy, operating costs, and debt. Cap rate and cash-on-cash keep going after rent.
How implied cap value works
Implied value is NOI divided by a comparison cap. \$36,000 of income at 6 percent is worth \$600,000. Offered at \$480,000, the gap is \$120,000 below that value.
How DSCR works
Debt service coverage divides net operating income by annual debt service. \$36,000 over \$24,000 is 1.5, so income can fall by a third and still pay the loan.
How net operating income works
NOI is gross rent minus vacancy minus operating expenses. On \$48,000 of rent with \$2,400 of vacancy and \$9,600 of costs it is \$36,000.
How the one percent rule works
The screen asks whether monthly rent reaches one percent of price. \$2,400 on \$240,000 is exactly 1 percent; \$2,000 on \$300,000 is 0.67.
Risk and insurance
Insurance and risk pooling explained
How pooling independent risks makes an unpredictable loss predictable for the group, why cover can still be worth buying when it loses money on average, and what deductibles change.
Life and disability insurance explained
Who needs life cover and who does not, why level term is the usual starting point, why a long disability is the more likely claim, and how to reason about the amount.
What liquidity means in finance
How fast an asset turns into cash without moving its price, why illiquid assets can pay more, and why running out of cash is not the same as running out of value.
How life insurance need is sized
Income replacement plus debts, minus assets and existing cover. On \$80,000 for ten years with \$200,000 of debt, the need is \$850,000.
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